Rethinking animal social complexity measures with the help of complex systems concepts Elizabeth A. Hobson1,*, Vanessa Ferdinand1,2, Artemy Kolchinsky1, and Joshua Garland1 1Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501 USA 2University of Melbourne, Parkville VIC 3010, Australia *Corresponding author Version Mar 15 2019, re-submitted to Animal Behaviour Abstract Explaining how and why some species evolved to have more complex social structures than others has been a long-term goal for many researchers in animal behavior because it would provide important insight into the links between evolution and ecology, sociality, and cognition. However, despite long-standing interest, the evolution of social complexity is still poorly understood. This may be due in part to researchers focusing on the feasibility of quantifying aspects of sociality, rather than what features are characteristic of animal social complexity in the first place. Any given approach to studying complexity can tell us some things about animal sociality, but may miss others, so it is critical to decide first how to conceptualize complexity before jumping in to quantifying it. Here, we briefly summarize five existing approaches to measuring social complexity. Then, we highlight three fundamental concepts that are commonly used in the field of complex systems: (1) scales of organization, (2) compression, and (3) emergence. All of these concepts are applicable to the study of animal social systems, but are not often explicitly addressed in existing social complexity measures. We discuss how these concepts can provide a rigorous foundation for conceptualizing social complexity, the potential benefits of incorporating them, and how existing measures do (or do not) include them. Ultimately, researchers need to critically evaluate any measure of animal social complexity in order to balance the biological relevance of the aspect of sociality they are quantifying with the feasibility of obtaining enough data. Keywords: Animal sociality, complex systems, coarse-graining, compression, downward causa- tion, emergence, feedback, self-organization, social scale, social structure arXiv:1812.01185v2 [physics.soc-ph] 20 Mar 2019 1 Highlights • The richness of animal social complexity is inherently challenging to quantify and current approaches fall short. • Fundamental concepts from complex systems theory (scales of organization, compression, and emergence), when coupled with traditional approaches, will lead to new insights and ways of thinking about animal social complexity. • Complex systems concepts may also be useful in moving beyond purely descriptive accounts of sociality and allowing practitioners to create causal accounts of animal social complexity. Introduction Social systems reflect the rich landscape and diversity of social solutions that animals have evolved in order to thrive in a wide range of habitats and conditions. These solutions vary in complexity, from apparently simple ones to those that appear more complex. Explaining how and why some species evolved to have more complex social structures than others has been a long- term goal for many researchers in animal behavior because it would provide important insight into the links between evolution and ecology, sociality, and cognition. However, despite long-standing interest, the evolution of social complexity is still poorly understood [1], largely due to disagree- ment about how to best quantify complexity, how to compare complexity across species, whether these broad comparisons are biologically meaningful, and what complexity is in the first place. In this paper, we critically consider which aspects of complexity we should incorporate in order to evaluate different approaches to social complexity. There are two major reasons to quantify animal social complexity, and these reasons can shape how social complexity is quantified. First, researchers are often drawn to making comparisons across groups, which we call the “different is interesting” motivation. When species systematically vary on some dimensions of their social organization, then that itself is something interesting to study, understand, and explain, and can indicate promising areas for future research. For exam- ple, if two bird species are very similar but one has group sizes of 10 while the other forms groups of over 1000, then it is intrinsically interesting to explain why those differences occur. Second, and especially relevant to social and cognitive research, is the “more is harder” motivation. For social systems, there is an implicit (or sometimes explicit) assumption that higher social complexity (how- ever it is measured) is inherently difficult to originate and maintain. This motivation is often framed in evolutionary terms, in that it is conjectured that natural selection produced special mechanisms that allows some species to form, maintain, and process more complex social systems. In this case, it is then interesting to identify those mechanisms and understand how they evolved. These two motivations have led to what we view as two different approaches to quantifying animal social complexity. We term these descriptive and causal approaches. This distinction parallels recent work that suggests that social complexity can be considered from an “insider’s” perspective versus an “outsider’s” perspective [2], but differs in that our distinction between descriptive and causal approaches is more general and not linked to analyses on a specific scale. Researchers driven by the “different is interesting” motivation generally approach measuring social systems 2 from an “outsider’s” perspective and quantify social complexity with a descriptive approach, which can allow researchers to compare these systems to one another. Researchers may want to use this descriptive approach to get a useful statistic to characterize societies, or as a quantitative measure of the amount of organization or amount of pattern in the collective behavior of groups of animals to facilitate comparisons of sociality across different species. Alternatively, researchers driven by the “more is harder” motivation take more of the perspective of animals within the society, and adopt a causal approach to animal social complexity. This causal approach is concerned with uncovering the processes or mechanisms that underlie the organization and complexity of societies. Causes of particular social patterns can range widely, across cognitive, perceptual, ecological, spatial, and physiological mechanisms. Researchers may use a causal approach to understand what types of information play a role in structuring social organization, or to gain insight into the cognitive abilities needed to support and function within a certain kind of social system. An important test of a causal approach is to see if it leads to quantitative generative models of animal societies that can replicate and predict aspects of real empirical data. There is an intimate link between these two approaches to animal social complexity: a descrip- tive approach may allow researchers to rank systems in terms of their relative complexity, while a causal approach can identify the mechanics that cause one system to be more or less com- plex than another. In many cases, scientists are interested in understanding the mechanisms underlying social behavior, but cannot observe those mechanisms directly, so may instead employ descriptive measures as proxies for reasoning about the causal mechanisms. Both descriptive and causal approaches to complexity, and their associated measures, operate on a continuum, with most actual measures of complexity being motivated by considerations that fall somewhere between these two extremes. Different types of social complexity measures are required in order to address particular study goals. One way to explicitly evaluate and compare different aspects of animal social complexity mea- sures, and whether they are suited for a particular study question, is to incorporate some of the fundamental concepts of complex systems theory. In the past 30 to 40 years, the field of com- plex systems has developed theories of how underlying microscopic interactions in distributed, multi-component systems give rise to novel properties at the macro-scale (for an approachable introduction to complexity and sociality, see [3]). Many of the fundamental concepts in the field of complex systems can guide thinking about the “amount” and “types” of social organization, and in this way help formalize intuitive notions of social complexity. However, most of these concepts have been largely isolated from research on animal behavior and animal sociality. A better understand- ing of some of the fundamental concepts in complex systems can help critically evaluate existing approaches to animal social complexity as well as suggest promising avenues for developing new approaches. Here, we summarize several existing measures of animal social complexity. We then highlight three foundational concepts that are commonly used in the field of complex systems: (1) scales of organization, (2) compression, and (3) emergence. We show how they can provide a rigorous foundation for approaching social complexity and how they can help circumvent some of the pit- falls of certain existing animal social complexity measures. Using these concepts from complex systems, we re-examine existing animal social complexity measures and show how they relate to 3 these fundamental concepts. Overview of social complexity measures Complex social systems